Question 1

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data.
-The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in meters) are listed below. $$\begin{array} { l l l l l l l } 
0.453 & 0.401 & 0.596 & 0.388 & 0.649 & 0.279 & 0.551
\end{array}$$
A) 1.6744 m
B) 1.5718 m
C) 0.388 m
D) 0.1308 m

Accepted Answer

The standard deviation is calculated using the formula for a sample: $\sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$. After calculating, the standard deviation is approximately 0.1308 m.

Question 2

Find the mean of the data summarized in the given frequency distribution.
-The test scores of 40 students are summarized in the frequency distribution below. Find the mean score. 
$$\begin{array} { c | c } 
\text { Score } & \text { Students } \
\hline 50 - 59 & 6 \
60 - 69 & 5 \
70 - 79 & 6 \
80 - 89 & 11 \
90 - 99 & 12
\end{array}$$
A) 71.1
B) 79.0
C) 74.5
D) 75.1

Accepted Answer

The answer of Find the mean of the data summarized...

Question 3

Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth.
-The heights in feet of people who work in an office are as follows. $$\begin{array} { l l l l l l l l l l } 
5.9 & 5.5 & 5.8 & 5.4 & 5.6 & 5.7 & 5.9 & 6.2 & 5.8 & 5.7
\end{array}$$
A) 1.2
B) 0.2
C) 0.1
D) 0.5

Accepted Answer

The range rule of thumb estimates the standard deviation as the range divided by 4. The range of the data is 6.2 - 5.4 = 0.8. Dividing by 4 gives 0.2.

Question 4

Provide an appropriate response.
-If all the values in a data set are converted to z-scores, the shape of the distribution of the z-scores will be the same as the distribution of the original data.

Accepted Answer

Converting data to z-scores only changes the scale of the data, but it does not change the shape or distribution. Therefore, the shape of the distribution of the z-scores will be the same as the distribution of the original data.

Question 5

The test scores of 40 students are listed below. Find $P _ { 85 }$.
$\begin{array} { l l l l l l l l l l } 30 & 35 & 43 & 44 & 47 & 48 & 54 & 55 & 56 & 57 \end{array}$
$\begin{array} { l l l l l l l l l l } 59 & 62 & 63 & 65 & 66 & 68 & 69 & 69 & 71 & 72 \end{array}$
$\begin{array} { l l l l l l l l l l } 72 & 73 & 74 & 76 & 77 & 77 & 78 & 79 & 80 & 81 \end{array}$
$\begin{array} { l l l l l l l l l l } 81 & 82 & 83 & 85 & 89 & 92 & 93 & 94 & 97 & 98 \end{array}$
A) 34
B) 89
C) 87
D) 85

Accepted Answer

The answer of The test scores of 40 students are...

Question 6

Use the empirical rule to solve the problem.
-The amount of Jen's monthly phone bill is normally distributed with a mean of $59 and a standard deviation of $8. What percentage of her phone bills are between $35 and $83?
A) 68%
B) 95%
C) 99.99%
D) 99.7%

Accepted Answer

The empirical rule states that 99.7% of data in a normal distribution lies within three standard deviations from the mean. $35 and $83 are three standard deviations below and above the mean ($59 ± 3*$8), respectively.

Question 7

Find the mode(s) for the given sample data.
-$$\begin{array} { l l l l l l l } 
7.14 & 7.41 & 7.56 & 7.14 & 7.88 & 7.99 & 7.62
\end{array}$$
A) 7.41
B) 7.14
C) 7.56
D) 7.534

Accepted Answer

The mode is the number that appears most frequently in a data set. In this data set, 7.14 appears twice, while all other numbers appear only once.

Question 8

When finding percentiles, if the locator L is not a whole number, one procedure is to interpolate so that a locator of 23.75, for example, leads to a value that is 3/4 of the way between the 23rd and 24th scores. Use this method of interpolation to find P75 for the set of test scores below. $$\begin{array} { l l l l l l } 
51 & 54 & 64 & 68 & 72 & 74 \
78 & 83 & 91 & 94 & 99 &
\end{array}$$
A) 83
B) 85
C) 87
D) 91

Accepted Answer

To find P75, calculate L = 0.75 * 11 = 8.25. Interpolate between the 8th (83) and 9th (91) scores: 83 + 0.25 * (91 - 83) = 85.

Question 9

Find the variance for the given data. Round your answer to one more decimal place than the original data.
-A class of sixth grade students kept accurate records on the amount of time they spent playing video games during a one-week period. The times (in hours) are listed below: $$\begin{array} { l l l l l } 
11.7 & 17.9 & 18.4 & 12.9 & 17.1 \
15.8 & 11.3 & 28.7 & 18.0 & 26.4
\end{array}$$
A) $147.46 \mathrm { hr } ^ { 2 }$
B) $30.11 \mathrm { hr } ^ { 2 }$
C) $33.46 \mathrm { hr } ^ { 2 }$
D) $33.36 \mathrm { hr } ^ { 2 }$

Accepted Answer

The answer of Find the variance for the given data....

Question 10

Find the percentile for the data value.
-In a data set with a range of 64.5 to 103 and 300 observations, there are 207 observations with values less than 88.5. Find the percentile for 88.5.
A) 116.38
B) 32
C) 69
D) 480

Accepted Answer

The percentile is calculated by dividing the number of observations below the data value by the total number of observations and then multiplying by 100. Here, (207/300) * 100 = 69.

Question 11

Determine which score corresponds to the higher relative position.
-Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150?
A) Both scores have the same relative position.
B) A score of 688
C) A score of 92

Accepted Answer

The answer of Determine which score corresponds to the higher...

Question 12

Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual.
Consider a score to be unusual if its z-score is less than -2.00 or greater than 2.00. Round the z-score to the nearest tenth if necessary.
-A test score of 50.2 on a test having a mean of 73 and a standard deviation of 12. A) $- 22.8$; unusual
B) $- 1.9$; not unusual
C) -1.9; unusual
D) $1.9$; not unusual

Accepted Answer

The answer of Find the z-score corresponding to the given...

Question 13

Find the variance for the given data. Round your answer to one more decimal place than the original data.
-The weights (in ounces) of 10 cookies are shown. $\begin{array} { c c c l c } 1.12 & 0.92 & 1.44 & 1.28 & 0.97 \ 1.03 & 1.14 & 0.85 & 1.4 & 0.95 \end{array}$

A) $0.042 \mathrm { oz } ^ { 2 }$
B) $0.038 \mathrm { oz } ^ { 2 }$
C) $0.034 \mathrm { oz } ^ { 2 }$
D) $0.032 \mathrm { oz } ^ { 2 }$

Accepted Answer

The answer of Find the variance for the given data....

Question 14

Find the range for the given sample data.
-Fred, a local mechanic, recorded the price of an oil and filter change at twelve competing service stations. The prices (in dollars) are shown below. $$\begin{array} { l l l l } 
32.99 & 24.95 & 26.95 & 28.95 \
18.95 & 28.99 & 30.95 & 22.95 \
24.95 & 26.95 & 29.95 & 28.95
\end{array}$$
A) $12.00
B) $14.04
C) $10.05
D) $32.99

Accepted Answer

The answer of Find the range for the given sample...

Question 15

Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values.
-Six college buddies bought each other Christmas gifts. They amounts they spent are shown below. $$\begin{array} { l l l } 
\$ 273.79 & \$ 264.48 & \$ 180.50 \
\$ 123.42 & \$ 188.27 & \$ 194.20
\end{array}$$ What was the mean amount spent? Round your answer to the nearest cent.
A) $244.93
B) $204.11
C) $232.93
D) $306.17

Accepted Answer

To find the mean, add all the amounts together and divide by the number of amounts: (273.79 + 264.48 + 180.50 + 123.42 + 188.27 + 194.20) / 6 = 204.11.

Question 16

Find the mode(s) for the given sample data.
-$$\begin{array} { l l l l l l l } 
20 & 36 & 46 & 36 & 49 & 36 & 49
\end{array}$$
A) 36
B) 46
C) 38.9
D) 49

Accepted Answer

36 appears three times, which is most frequent.

Question 17

Find the mean of the data summarized in the given frequency distribution.
-The highway speeds of 100 cars are summarized in the frequency distribution below. Find the mean speed.
$$\begin{array} { r | r } 
\text { Speed (mph) } & \text { Cars } \
\hline 30 - 39 & 3 \
40 - 49 & 16 \
50 - 59 & 52 \
60 - 69 & 16 \
70 - 79 & 13
\end{array}$$  
A) 59.3 mph
B) 56.5 mph
C) 62.2 mph
D) 54.5 mph

Accepted Answer

To find the mean, calculate the midpoint for each speed interval, multiply by the frequency, sum these products, and divide by the total number of cars. The calculation is: [(34.5*3) + (44.5*16) + (54.5*52) + (64.5*16) + (74.5*13)] / 100 = 56.5 mph.

Question 18

Elaine gets quiz grades of 60, 86, and 78. She gets a 70 on her final exam. Find the weighted mean if the quizzes each count for 20% and the final exam counts for 40% of the final grade. Round to one decimal place.
A) 70.8
B) 72.3
C) 73.5
D) 72.8

Accepted Answer

Weighted mean = (0.2 * 60) + (0.2 * 86) + (0.2 * 78) + (0.4 * 70) = 72.8

Question 19

Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth.
-The maximum value of a distribution is 42.7 and the minimum value is 2.3.
A) 15.1
B) 10.1
C) 7.1
D) 14.7

Accepted Answer

The range rule of thumb estimates the standard deviation as the range divided by 4. The range is 42.7 - 2.3 = 40.4. Dividing by 4 gives 10.1.

Question 20

The data below consists of the heights (in inches) of 20 randomly selected women. Find the 10% trimmed mean of the data set. The 10% trimmed mean is found by arranging the data in order, deleting the bottom 10% of the values and the top 10% of the values and then calculating the mean of the remaining values. 
$$\begin{array} { l l l l l l l l l l } 
65 & 65 & 63 & 61 & 63 & 67 & 70 & 67 & 62 & 63 \
61 & 66 & 75 & 67 & 60 & 59 & 64 & 68 & 65 & 71
\end{array}$$
A) 65.1 in.
B) 64.9 in.
C) 64.8 in.
D) 51.9 in.

Accepted Answer

The answer of The data below consists of the heights...

Quiz 3: Statistics for Describing, Exploring, and Comparing Data

Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth. -The heights in feet of people who work in an office are as follows. $\begin{array} { l l l l l l l l l l } 5.9 & 5.5 & 5.8 & 5.4 & 5.6 & 5.7 & 5.9 & 6.2 & 5.8 & 5.7\end{array}$

Provide an appropriate response. -If all the values in a data set are converted to z-scores, the shape of the distribution of the z-scores will be the same as the distribution of the original data.

Use the empirical rule to solve the problem. -The amount of Jen's monthly phone bill is normally distributed with a mean of $59 and a standard deviation of $8. What percentage of her phone bills are between $35 and $83?

Find the mode(s) for the given sample data. - $\begin{array} { l l l l l l l } 7.14 & 7.41 & 7.56 & 7.14 & 7.88 & 7.99 & 7.62\end{array}$

Find the percentile for the data value. -In a data set with a range of 64.5 to 103 and 300 observations, there are 207 observations with values less than 88.5. Find the percentile for 88.5.

Determine which score corresponds to the higher relative position. -Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150?

Find the mode(s) for the given sample data. - $\begin{array} { l l l l l l l } 20 & 36 & 46 & 36 & 49 & 36 & 49\end{array}$

Elaine gets quiz grades of 60, 86, and 78. She gets a 70 on her final exam. Find the weighted mean if the quizzes each count for 20% and the final exam counts for 40% of the final grade. Round to one decimal place.

Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth. -The maximum value of a distribution is 42.7 and the minimum value is 2.3.